Module 4, Lesson 1 Online Algebra VHS@PWCS Intro To Functions Module 4, Lesson 1 Online Algebra VHS@PWCS

This is an important skill that we will use a lot from hear on out. Graphing review If you cannot remember how to graph points on a coordinate plane from Pre-Algebra, then you can do one of 2 things or both! Review page 58 in your textbook. Look at the video title graphing review This is an important skill that we will use a lot from hear on out.

Relations In algebra a relation is a set of ordered pairs. They do not have to have a rule, but can be any set of ordered pairs. Because we are talking about sets, we need to use braces { }. Braces mean all of these things are in a set. An example of a relation is below: {(3, 2), (0, 0), (4, 9), (-3, -7)}

Different Ways To Show Relations. One of the ways to show the relation {(4, 5), (4, 2), (-1, -1), (2, -1)} is a mapping. Each x- value MAPS to a y-value. The arrows show us the ordered pairs. Notice that x-coordinate of 4 has two y – values (2 and 5), but 4 is used once, but the two arrows indicate the different ordered pairs. X – coordinates Y – Coordinates -1 2 4 -1 2 5

Different Ways To Show Relations Two other ways to show the relation {(4, 5), (4, 2), (-1, -1), (2, -1)} are a table and a graph. (4, 5) Graph: Table: X Y -1 2 4 5 (4, 2) (-1, -1) (2, -1)

A relation is made up of domain and a range. Domain and Range A relation is made up of domain and a range. The Domain is the set of all x-coordinates. Other names for the domain are independent variables and input. The Range is the set of all y-coordinates. Other names for the range are dependent variables and output.

Domain and Range What is the domain and range of the following relation? Domain: {-1, 2, 4} Notice that even though there are two fours, we only state it once. We also used braces because the domain is a set. Range: {-1, 2, 5} Notice that even though there are two negative ones, we only state it once. We also used braces because the range is a set. X Y -1 2 4 5

Relation Review A relation is a set of ordered pairs. The can be displayed 4 different ways Set of ordered pairs Mapping Table Graph A relation is made up of a domain and range. The domain is all the x-coordinates Other names for the domain are: independent variables and input The range is all the y-coordinates. Other names for the range are: dependent variables and output.

Functions A function is a special relation. A function assigns exactly one value of the dependent variable to each value of the independent variable. In other words each x – coordinate maps to only 1 y-coordinate.

How To Tell if a Relation is a Function. In a table or set of ordered pairs, if an x-value repeats then it is not a function. X Y -1 2 4 5 X Y -1 2 6 -5 10 Notice the 4 repeats, so it is not a function! In this relation, no x-values repeat, so this is a function. It is okay for y-values to repeat.

How To Tell if a Relation is a Function. In a mapping each x, should have only 1 arrow coming from it. X 2 4 Y -2 -1 X 2 4 6 Y -2 -1 This is a function This is not a function

Different Ways To Show Relations In a graph, we use a vertical line test. If the graph passes through the vertical line more than once it is not a function. The vertical line goes through the graph at 2 places it is not a function. Here no matter where we draw a vertical line, that line will only go through our graph once. So this is a function.

Which of the following are functions? {(0, 2), (1, 2) (3, 2)} x 1 3 y -2 4 Only the set of ordered pairs is a function, in both the table and the mapping there is an x that repeats and the graph fails the vertical line test. x 3 4 Y -1 3

Function Review Remember that a function is a special relation where each member of the domain maps to exactly one member of the range. Other names for the domain are: x-coordinates, input, independent variable Other names for the range are: y-coordinates, output, dependent variable.